Internationally, O'Connell, who captained the Lions in 2007, has never beaten New Zealand - the Lions' opponents in 2017 - but Ireland came might close in autumn, only to slip to a 24-22 defeat.
And O'Connell expects the challenge to be just as tough this weekend.
"When Rob (Penney) talks about going beyond where you've gone before, it's being ready for that challenge, it's being ready to do that and be prepared to do that. From a fitness point of view, maybe sometimes it's easy to be prepared for that, but mentally to be prepared for everything they're going to throw at you," he said.
"To be prepared for periods when you're under the cosh and just have to dig in and hang in there... That's a big thing.
"It's kind of like the feeling you get the week before you play New Zealand (with Ireland). If guys aren't prepared to go beyond where they've been all season, you know you could almost end up getting embarrassed.
"We know that we have to be at the very best of our ability. We have to play to the best of our ability from one to 23 to be in with a chance of winning the game. And we probably need them to have a little bit of an off day - and that's a simple fact."